If `y=e^-x cos x`, show that `(d^2y)/(dx^2)= 2e^-x sin x`

Explanation

To solve the problem, we need to find the second derivative of the function \( y = e^{-x} \cos x \) and show that it equals \( 2 e^{-x} \sin x \).

### Step 1: Find the first derivative \( \frac{dy}{dx} \)

We will use the product rule for differentiation, which states that if \( u \) and \( v \) are functions of \( x \), then:

\[
\frac{d(uv)}{dx} = u \frac{dv}{dx} + v \frac{du}{dx}
...